Department of Mathematics, Institute for Advanced Studies in Basic Sciences, Zanjan, I. R. of Iran
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15914, I. R. of Iran
–A notion of amenability for topological semigroups is introduced. A topological semigroup S is
called Johnson amenable if for every Banach S -bimodule E , every bounded crossed homomorphism from
S to E* is principal. In this paper it is shown that a discrete semigroup S is Johnson amenable if and only if
1(S) is an amenable Banach algebra. Also, we show that if a topological semigroup S is Johnson amenable,
then it is amenable, but the converse is not true.